An application of the Kantorovich theoremto nonlinear finite element analysis
An application of the Kantorovich theoremto nonlinear finite element analysis
复制标题
康托罗维奇定理在非线性有限元分析中的应用
DOI：
10.1007/s002110050466
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发表时间：
1999
影响因子：
2.1
通讯作者：
T. Tsuchiya
中科院分区：
文献类型：
--
作者：
T. Tsuchiya
总结。研究了强非线性椭圆型边值问题的有限元解。本文利用Kantorovich定理证明了，如果由边值问题定义的非线性算子的Fréchet导数在精确解上同构，则在精确解附近存在局部唯一的有限元解。此外，还得到了几个先验误差估计。
Summary. Finite element solutions of strongly nonlinear elliptic boundary value problems are considered. In this paper, using the Kantorovich theorem, we show that, if the Fréchet derivative of the nonlinear operator defined by the boundary value problem is an isomorphism at an exact solution, then there exists a locally unique finite element solution near the exact solution. Moreover, several a priori error estimates are obtained.